Finite Group Databasebeta

← #17963174

Subgroups — #17963174

Order 4352.

2166 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763751C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14543969C214yesmaximal, complemented
4#14543963C214yesmaximal, complemented
5#14543958C212yesmaximal
6#14543958C212yesmaximal
7C22×C4⋊C4×D17C211yesmaximal, characteristic
8C22×C4⋊#595C2212yes—
9C22×C22⋊#595C2212yes—
10C22×C22⋊#595C2212yes—
11C22×C4×#595C2212yes—
12#11763751—24no—
13C4×C22⋊#595—24no—
14C2×(C2×#595)⋊C4C2212yes—
15C2×(C2×#595)⋊C4C2212yes—
16C2×(C2×#595)⋊C4C2218yes—
17C2×(C2×#595)⋊C4C2218yes—
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C22×C4⋊Dic17C411yescharacteristic, complemented
22C22×#63225C411yescharacteristic, complemented
23C22×#63225C411yescharacteristic, complemented
24C2×C4⋊C4×D17—24no—
25C2×C4⋊C4×D17—24no—
26C2×C4⋊C4×D17C412yescomplemented
27C2×C4⋊C4×D17C412yescomplemented
28C2×C4⋊C4×D17C2212yes—
29C2×C4⋊C4×D17C2212yes—
30C22×C4⋊C4×C17C411yescharacteristic, complemented
31C24×D17C2311yescharacteristic
32C23×#595C2314yes—
33C23×#595C2314yes—
34C23×C4×C17C2×C411yescharacteristic
35C23×C4×C17C2×C411yescharacteristic
36C23×C4×C17C2×C411yescharacteristic
37C23×Dic17C2×C411yescharacteristic
38C23×Dic17C2×C411yescharacteristic
39C23×Dic17C2×C411yescharacteristic
40C22×C4×D17—22no—
41C22×C4×D17—22no—
42C22×C4×D17—28no—
43C22×C4×D17—22no—
44C22×C4×D17—22no—
45C22×C4×D17—44no—
46C22×C4×D17—44no—
47C22×C4×D17C2×C412yes—
48C22×C4×D17C2×C412yes—
49C22×C4×D17C2×C411yescharacteristic
50C22×C4×D17C2×C411yescharacteristic
51C22×C4×D17D414yes—
52C22×C4×D17D414yes—
53C22×C4×D17C2312yes—
54C22×C4×D17C2311yescharacteristic
55C22×C4×D17C2311yescharacteristic
56C22×C4×D17C2312yes—
57C2×C22⋊#595—24no—
58C2×C22⋊#595—24no—
59C2×C22⋊#595—24no—
60C2×C22⋊#595—28no—
61C2×C22⋊#595Q818yes—
62C2×C4⋊#595—24no—
63C2×C4⋊#595—44no—
64C2×C4×#595—24no—
65C2×C4×#595—44no—
66C2×C4⋊C4×C17—24no—
67C2×C4⋊C4×C17C2×C412yes—
68C2×C4⋊C4×C17C2×C412yes—
69C2×C4⋊Dic17—24no—
70C2×C4⋊Dic17C2×C412yes—
71C2×C4⋊Dic17C2×C412yes—
72C2×#63225—24no—
73C2×#63225—24no—
74C2×#63225C2×C412yes—
75C2×#63225C2×C412yes—
76C2×#63225C2×C412yes—
77C2×#63225C2×C412yes—
78C4⋊C4×D17—28no—
79C4⋊C4×D17—28no—
80C4⋊C4×D17—24no—
81C4⋊C4×D17—24no—
82C4⋊C4×D17—24no—
83C4⋊C4×D17—24no—
84(C2×#595)⋊C4—24no—
85(C2×#595)⋊C4—24no—
86(C2×#595)⋊C4—216no—
87(C2×#595)⋊C4—48no—
88C24×C17C22×C411yescharacteristic
89C23×D17—24no—
90C23×D17—24no—
91C23×D17C22×C411yescharacteristic
92C23×D17C2×D412yes—
93C23×D17C2×D412yes—
94C23×D17C2×Q814yes—
95C23×D17#4114yes—
96C23×D17C2411yescharacteristic
97C22×#595—24no—
98C22×#595—24no—
99C22×#595—28no—
100C22×#595—28no—
101C22×#595—24no—
102C22×#595—28no—
103C22×#595—28no—
104C22×#595—28no—
105C22×#595C2×Q818yes—
106C22×C4×C17—22no—
107C22×C4×C17—24no—
108C22×C4×C17—22no—
109C22×C4×C17—42no—
110C22×C4×C17—42no—
111C22×C4×C17C22⋊C414yes—
112C22×C4×C17C22×C412yes—
113C22×C4×C17C22×C411yescharacteristic
114C22×C4×C17C22×C411yescharacteristic
115C22×C4×C17C22×C412yes—
116C22×Dic17—22no—
117C22×Dic17—24no—
118C22×Dic17—22no—
119C22×Dic17—42no—
120C22×Dic17—42no—
121C22×Dic17C22⋊C414yes—
122C22×Dic17C22×C412yes—
123C22×Dic17C22×C411yescharacteristic
124C22×Dic17C22×C411yescharacteristic
125C22×Dic17C22×C412yes—
126C2×C4×D17—216no—
127C2×C4×D17—216no—
128C2×C4×D17—24no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—24no—
132C2×C4×D17—24no—
133C2×C4×D17—24no—
134C2×C4×D17—24no—
135C2×C4×D17—24no—
136C2×C4×D17—24no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—28no—
140C2×C4×D17—48no—
141C2×C4×D17—48no—
142C2×C4×D17—42no—
143C2×C4×D17—42no—
144C2×C4×D17—44no—
145C2×C4×D17—48no—
146C2×C4×D17—48no—
147C2×C4×D17C22⋊C414yes—
148C2×C4×D17C22⋊C414yes—
149C2×C4×D17C2×D412yes—
150C2×C4×D17C2×D412yes—
151C2×C4×D17C2×D412yes—
152C2×C4×D17C2×D412yes—
153C2×C4×D17#4118yes—
154C22⋊#595—216no—
155C22⋊#595—48no—
156C4⋊#595—48no—
157C4×#595—48no—
158C4⋊C4×C17—24no—
159C4⋊C4×C17—24no—
160C4⋊Dic17—24no—
161C4⋊Dic17—24no—
162#63225—24no—
163#63225—24no—
164#63225—24no—
165#63225—24no—
166#13923—171nomaximal, Sylow
167C23×C17—22no—
168C23×C17—22no—
169C23×C17C2×C22⋊C412yes—
170C23×C17C4×Q814yes—
171C23×C17C23×C411yescharacteristic
172C22×D17—22no—
173C22×D17—22no—
174C22×D17—24no—
175C22×D17—24no—
176C22×D17—24no—
177C22×D17—24no—
178C22×D17—216no—
179C22×D17—216no—
180C22×D17C2×C22⋊C412yes—
181C22×D17C4×Q814yes—
182C22×D17C22⋊Q818yes—
183C22×D17#12414yes—
184C22×D17C4⋊Q814yes—
185C22×D17C22×D411yescharacteristic
186C22×D17C22×D411yescharacteristic
187C22×D17C22×Q812yes—
188C22×D17C2×#4112yes—
189C22×D17C2×#4114yes—
190C22×D17H(5,𝔽2)14yes—
191C2×#595—28no—
192C2×#595—216no—
193C2×#595—44no—
194C2×#595—44no—
195C2×#595—48no—
196C2×#595—44no—
197C2×#595—44no—
198C2×#595—44no—
199C2×#595—416no—
200C2×C4×C17—28no—
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—24no—
207C2×C4×C17—44no—
208C2×C4×C17—44no—
209C2×C4×C17C2×C22⋊C412yes—
210C2×C4×C17C2×C22⋊C412yes—
211C2×C4×C17#11714yes—
212C2×Dic17—28no—
213C2×Dic17—22no—
214C2×Dic17—22no—
215C2×Dic17—22no—
216C2×Dic17—22no—
217C2×Dic17—22no—
218C2×Dic17—24no—
219C2×Dic17—44no—
220C2×Dic17—44no—
221C2×Dic17C2×C22⋊C412yes—
222C2×Dic17C2×C22⋊C412yes—
223C2×Dic17#11714yes—
224C4×D17—216no—
225C4×D17—28no—
226C4×D17—28no—
227C4×D17—24no—
228C4×D17—24no—
229C4×D17—24no—
230C4×D17—24no—
231C4×D17—44no—
232C4×D17—44no—
233C4×D17—48no—
234C4×D17—44no—
235C4×D17—44no—
236C23×C4⋊C4—171no—
237C2×#380—171no—
238C2×C4×C22⋊C4—171no—
239#1441—174no—
240#1436—174no—
241C22⋊#95—172no—
242C22⋊#95—172no—
243C22×C17—22no—
244C22×C17—28no—
245C22×C17—22no—
246C22×C17#39114yes—
247C22×C17C22×C22⋊C411yescharacteristic
248C22×C17C2×#11712yes—
249C22×C17C2×C4×Q812yes—
250C22×C17#51812yes—
251C2×D17—22no—
252C2×D17—28no—
253C2×D17—22no—
254C2×D17—216no—
255C2×D17—28no—
256C2×D17—28no—
257C2×D17#39114yes—
258C2×D17C2×C22⋊Q812yes—
259C2×D17#52512yes—
260C2×D17#52512yes—
261C2×D17C2×#12411yescharacteristic
262C2×D17C2×C4⋊Q811yescharacteristic
263C2×D17#53412yes—
264C2×D17#53412yes—
265C2×D17#55318yes—
266C2×D17#55418yes—
267#595—48no—
268#595—84no—
269C4×C17—22no—
270C4×C17—22no—
271C4×C17—24no—
272C4×C17—42no—
273Dic17—22no—
274Dic17—22no—
275Dic17—24no—
276Dic17—42no—
277C24×C4—171no—
278C24×C4—171no—
279C24×C4—171no—
280C22×C4⋊C4—171no—
281C22×C4⋊C4—171no—
282C22×C4⋊C4—171no—
283C22×C4⋊C4—172no—
284C22×C4⋊C4—172no—
285C22×C4⋊C4—172no—
286C22×C4⋊C4—172no—
287C22×C4⋊C4—172no—
288C22×C4⋊C4—344no—
289C22×C4⋊C4—344no—
290C22×C4⋊C4#59511yescharacteristic, complemented
291C22×C22⋊C4—172no—
292C22×C22⋊C4—172no—
293C22×C42—172no—
294#380—344no—
295C4×C22⋊C4—344no—
296C2×#95—178no—
297C2×#95—172no—
298C2×#95—172no—
299C2×#95—178no—
300C2×C17—24no—
301C2×C17#228011yescharacteristic
302C2×C17C2×#39111yescharacteristic
303C2×C17#230811yescharacteristic
304C2×C17#234514yes—
305D17—24no—
306D17#257914yes—
307D17#258312yes—
308D17#259112yes—
309C25—171no—
310C23×C4—171no—
311C23×C4—171no—
312C23×C4—172no—
313C23×C4—171no—
314C23×C4—174no—
315C23×C4—174no—
316C23×C4—171no—
317C23×C4—171no—
318C23×C4—174no—
319C23×C4—171no—
320C23×C4—171no—
321C23×C4—172no—
322C23×C4—172no—
323C23×C4—172no—
324C23×C4—174no—
325C23×C4—348no—
326C23×C4—342no—
327C23×C4—342no—
328C23×C4—342no—
329C23×C4—342no—
330C23×C4—684no—
331C23×C4—684no—
332C23×C4C2×#59511yescharacteristic
333C23×C4C2×#59511yescharacteristic
334C23×C4C2×#59511yescharacteristic
335C2×C4⋊C4—24no—
336C2×C4⋊C4—172no—
337C2×C4⋊C4—172no—
338C2×C4⋊C4—172no—
339C2×C4⋊C4—172no—
340C2×C4⋊C4—172no—
341C2×C4⋊C4—172no—
342C2×C4⋊C4—344no—
343C2×C4⋊C4—344no—
344C2×C4⋊C4—344no—
345C2×C4⋊C4—344no—
346C2×C4⋊C4—348no—
347C2×C4⋊C4—348no—
348C2×C4⋊C4—344no—
349C2×C4⋊C4—344no—
350C2×C4⋊C4—344no—
351C2×C4⋊C4—344no—
352C2×C4⋊C4—684no—
353C2×C4⋊C4C2×#59512yes—
354C2×C4⋊C4C2×#59512yes—
355C2×C22⋊C4—178no—
356C2×C22⋊C4—344no—
357C2×C22⋊C4—344no—
358C2×C22⋊C4—348no—
359C2×C22⋊C4—344no—
360C2×C42—344no—
361C2×C42—684no—
362#95—344no—
363#95—344no—
364#95—3416no—
365#95—688no—
366C17#1392311yescharacteristic, complemented, Sylow
367C24—171no—
368C24—174no—
369C24—174no—
370C24—172no—
371C24—172no—
372C24—171no—
373C24—344no—
374C24—344no—
375C24C22×#59511yescharacteristic
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—171no—
382C22×C4—171no—
383C22×C4—172no—
384C22×C4—174no—
385C22×C4—178no—
386C22×C4—172no—
387C22×C4—172no—
388C22×C4—172no—
389C22×C4—172no—
390C22×C4—174no—
391C22×C4—174no—
392C22×C4—178no—
393C22×C4—172no—
394C22×C4—344no—
395C22×C4—344no—
396C22×C4—342no—
397C22×C4—342no—
398C22×C4—344no—
399C22×C4—344no—
400C22×C4—344no—
401C22×C4—3416no—
402C22×C4—3416no—
403C22×C4—348no—
404C22×C4—342no—
405C22×C4—342no—
406C22×C4—344no—
407C22×C4—344no—
408C22×C4—342no—
409C22×C4—344no—
410C22×C4—344no—
411C22×C4—348no—
412C22×C4—348no—
413C22×C4—344no—
414C22×C4—342no—
415C22×C4—344no—
416C22×C4—348no—
417C22×C4—348no—
418C22×C4—348no—
419C22×C4—682no—
420C22×C4—682no—
421C22×C4—684no—
422C22×C4—688no—
423C22×C4—688no—
424C22×C4—688no—
425C22×C4—688no—
426C22×C4—682no—
427C22×C4—682no—
428C22×C4C22⋊#59514yes—
429C22×C4C22×#59512yes—
430C22×C4C22×#59512yes—
431C22×C4C22×#59511yescharacteristic
432C22×C4C22×#59511yescharacteristic
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—344no—
436C4⋊C4—344no—
437C4⋊C4—344no—
438C4⋊C4—344no—
439C4⋊C4—344no—
440C4⋊C4—344no—
441C4⋊C4—688no—
442C22⋊C4—3416no—
443C22⋊C4—688no—
444C42—688no—
445C23—22no—
446C23—22no—
447C23—171no—
448C23—171no—
449C23—174no—
450C23—172no—
451C23—172no—
452C23—174no—
453C23—178no—
454C23—174no—
455C23—174no—
456C23—172no—
457C23—174no—
458C23—344no—
459C23—344no—
460C23—344no—
461C23—344no—
462C23—3416no—
463C23—3416no—
464C23—342no—
465C23—342no—
466C23Q8×#59514yes—
467C23C2×C22⋊#59512yes—
468C23C23×#59511yescharacteristic
469C2×C4—28no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—172no—
479C2×C4—172no—
480C2×C4—174no—
481C2×C4—344no—
482C2×C4—344no—
483C2×C4—348no—
484C2×C4—348no—
485C2×C4—344no—
486C2×C4—344no—
487C2×C4—3416no—
488C2×C4—348no—
489C2×C4—342no—
490C2×C4—342no—
491C2×C4—342no—
492C2×C4—342no—
493C2×C4—348no—
494C2×C4—3416no—
495C2×C4—342no—
496C2×C4—344no—
497C2×C4—684no—
498C2×C4—684no—
499C2×C4—684no—
500C2×C4—684no—
501C2×C4—688no—
502C2×C4—684no—
503C2×C4—684no—
504C2×C4—684no—
505C2×C4—684no—
506C2×C4—688no—
507C2×C4—684no—
508C2×C4—684no—
509C2×C4—684no—
510C2×C4—6816no—
511C2×C4#1058767714yes—
512C2×C4C2×C22⋊#59512yes—
513C2×C4C2×C22⋊#59512yes—
514C22—22no—
515C22—22no—
516C22—28no—
517C22—172no—
518C22—172no—
519C22—172no—
520C22—171no—
521C22—171no—
522C22—172no—
523C22—172no—
524C22—178no—
525C22—178no—
526C22—174no—
527C22—3416no—
528C22—348no—
529C22—348no—
530C22—342no—
531C22—342no—
532C22—348no—
533C22(C2×#595)⋊Q814yes—
534C22C22×C22⋊#59511yescharacteristic
535C22C2×#1058767712yes—
536C22C2×Q8×#59512yes—
537C22#1176387612yes—
538C4—24no—
539C4—22no—
540C4—22no—
541C4—42no—
542C4—344no—
543C4—342no—
544C4—342no—
545C4—688no—
546C4—682no—
547C4—1364no—
548C2—24no—
549C2—174no—
550C2—172no—
551C2—172no—
552C2—344no—
553C2#1454522811yescharacteristic
554C2C2×(C2×#595)⋊Q811yescharacteristic
555C2#1454525611yescharacteristic
556C2#1454529314yes—
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC22×C4⋊C4×C17C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenterC22×C4⋊C4#595
hypocenterC17#13923
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14543969C2semidirect
4. #14543963C2semidirect
21. C22×C4⋊Dic17C4semidirect
22. C22×#63225C4semidirect
23. C22×#63225C4semidirect
26. C2×C4⋊C4×D17C4semidirect
27. C2×C4⋊C4×D17C4semidirect
30. C22×C4⋊C4×C17C4semidirect
290. C22×C4⋊C4#595semidirect
366. C17#13923semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117637512
C2×C4×C22⋊#5952
#145439692
#145439632
#145439582
C22×C4⋊C4×D172
#1392317